Drag each tile to the correct box. Arrange the equations in order from least to greatest bed on their solution. Equation A: 5( x-6)+3x=3/4(2x-8) Equation B: 2.7(5.1x+4.9)=3.2+28.9 Equation C: 5(11x-18)=3(2x+7)

We will see that the probability of not winning the prize is equal to 0.38, so the correct option is b.

In this experiment, we have two possible outcomes.

One outcome is winning the prize, with a probability P and the other outcome is losing, with a probability Q.

Because there are only two outcomes we will have that:

P + Q  = 1

We know that P = 0.62, replacing that we get:

0.62 + Q = 1

Q = 1 - 0.62 = 0.38

So we conclude that the probability of not winning the prize is 0.38, then the correct option is b.

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Answer:

see explanation

Step-by-step explanation:

Given

P(x) = x³ + 7x² + 4x, then

P(a) = a³ + 7a² + 4a ← substitute x = a into polynomial

To evaluate P(- 2) substitute a = - 2 into P(a)

P(- 2) = (- 2)³ + 7(- 2)² + 4(- 2) = - 8 + 28 - 8 = 12

Since P(- 2) ≠ 0 then (x + 2) is not a factor of P(x)

Answer:

12

Step-by-step explanation:

(-2)³ + 7(-2)² + 4(-2)

12

Answer:

The answer on Plato is C as this is a final product

Step-by-step explanation:

These are the choices on Plato

A. wood

B. steel

C. needle

I would personally go w/ b or c

There is exactly one solution for this triangle, and the correct answer is:  b. 1 solution

To determine the number of solutions for the given triangle with angles A, C, and side c, we can use the Law of Sines, which states that in any triangle:

[tex]\[\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}\][/tex]

 Given:

- Angle A = 90 degrees (since it is a right angle, we assume A is the right angle for the purpose of this solution)

- Angle C = 4 degrees

- Side c = 12 units (opposite to angle C)

Since angle A is 90 degrees, we know that this triangle is a right-angled triangle. In a right-angled triangle, the other two angles must add up to 90 degrees. We are given one of those angles, C, which is 4 degrees. Therefore, the third angle, B, which is opposite side b, can be calculated as:

[tex]\[B = 90^\circ - C = 90^\circ - 4^\circ = 86^\circ\][/tex]

 Now, we have all three angles: A = 90°, B = 86°, and C = 4°. The sum of angles in any triangle is 180 degrees, and in this case:

[tex]\[A + B + C = 90^\circ + 86^\circ + 4^\circ = 180^\circ\][/tex]

 This confirms that the angles are consistent with the angles of a triangle.

Next, we can find the length of side b using the Law of Sines:

[tex]\[\frac{\sin(B)}{b} = \frac{\sin(C)}{c}\][/tex]

[tex]\[\frac{\sin(86^\circ)}{b} = \frac{\sin(4^\circ)}{12}\][/tex]

Since 86° and 4° are acute angles and sine of an acute angle is unique, there will be a unique positive value for b. This means there is only one possible length for side b that will satisfy the conditions of the triangle.

 Therefore, there is exactly one solution for this triangle, and the correct answer is:

b. 1 solution

[tex]\bf \lim\limits_{x\to 3}~-x^2+6x-8\implies \lim\limits_{x\to 3}~-(3)^2+6(3)-8\implies 1[/tex]

Answer:

2///////////////////////////

P(5,2) =  n! /(n-r)!

n = 5, r = 2:

= (5 x 4 x 3 x 2 x 1 ) /  3 x 2 x 1

Cancel out common factors:

= 5 x 4 = 20

The answer is 20.

Answer:

P (5,2) = 20

Step-by-step explanation:

First of all, we must understand two basic concepts:

A permutation is the variation of the order or position of the elements of an ordered set or a tuple.

The factorial function (symbol:!) Means that descending numbers are multiplied.

The formula to solve the permutation is:

[tex]\frac{n!}{(n-r)!}[/tex]

where "n" is the number of things you can choose, and you choose "r" from them (it cannot be repeated, order matters).

In the given case ...

P (n, r) = [tex]\frac{n!}{(n-r)!}[/tex]

Being n = 5, and r = 2

[tex]P(5,2)=\frac{5!}{(5-2)!}=\frac{5!}{3!}=\frac{5*4*3!}{3!}=5*4=20[/tex]

P (5,2) = 20

-------------------------------------------------- ----------------------------

I hope this helps!

Answer:

a model is an estimate or approximation of a data set. In the real world, there are too many variables to know exactly what will happen. However, if a model is a good fit, then it can be used to make predictions about what will happen. With a useful model, a predicted value should be a good estimate of an observed value.

Step-by-step explanation:

Took the assignment

George Box's statement "All models are wrong, but some are useful" suggests that while models are imperfect, they still offer valuable insights and utility in understanding complex systems.

George Box's statement "All models are wrong, but some are useful" acknowledges the inherent imperfections of models, emphasizing that they are simplified representations of reality.

Models, by nature, cannot perfectly capture every detail of a complex system.

However, despite their inaccuracies, models still hold utility in providing insights and aiding decision-making processes.

This perspective suggests that while models may not be entirely accurate, they can still offer valuable understanding and predictive power.

Box's statement encourages a balanced approach, where users recognize the limitations of models while leveraging their practical usefulness.

In essence, it underscores the importance of not dismissing models due to their imperfections but rather using them judiciously in specific contexts where they can provide meaningful insights.

Answer:

Step-by-step explanation:

Let s represent the length of the shorter part (in feet). Then the longer part has length (s+1), and the total length of the two parts is ...

  s + (s+1) = 25

  2s = 24 . . . . . . . subtract 1, simplify

  s = 12 . . . . . . . . . divide by 2; the length of the shorter part

  s+1 = 13 . . . . . . . the length of the longer part

The shorter part is 12 feet long; the longer part is 13 feet long.

_____

Comment on this problem type

You will note that the smaller number is half the difference of the total length (25) and the difference in lengths (1). This is the generic solution to a "sum and difference" problem. The smaller number is half the difference of the given numbers, and the larger number is half their sum: (25+1)/2 = 13.

Answer:

8 and 17

Step-by-step explanation:

Let's say the smaller number is x. The question says "The longer part is one foot more than twice the shorter part" so we reverse that using x which becomes x+2x+1=25 and x=8 so 8+8*2+1=25 => 8+17=25 so the answer is 8 and 17, please like and 5 star rate

Let [tex]x[/tex] be the amount (gal) of the 40% slime solution you end up using. You want to end up with 120 gal of the 50% solution, so that you would use [tex]120-x[/tex] gal of the 70% solution.

You want the final solution to consist of 50% slime, or 60 gal of slime. Each gal of the 40% solution contributes 0.4 gal of slime, while each gal of the 70% solution contributes 0.7 gal of slime. This means

[tex]0.4x+0.7(120-x)=0.5\cdot120=60[/tex]

[tex]\implies0.4x+84-0.7x=60[/tex]

[tex]\implies24=0.3x[/tex]

[tex]\implies x=80[/tex]

so the answer is B.

Answer:

Step-by-step explanation:

[tex]\text{We have the recursive formula of a series:}\\\\a_1=5\\a_n=3a_{n-1}\\\\a_2=3a_{2-1}=3a_1\to a_2=3(5)=15\\\\a_3=3a_{3-2}=3a_2\to a_3=3(15)=45\\\\a_4=3a_{4-1}=3a_3\to a_4=3(45)=135[/tex]

Answer:

For the equation

1) [tex]9 + | 2x - 3 | = 7[/tex]

x=0.5 and x=2.5

For the equation

2) [tex]3 + | 2x - 4 | = 15[/tex]

x=8 and x=-4

Step-by-step explanation:

For the equation

1) [tex]9 + | 2x - 3 | = 7[/tex]

we have 2 cases

Case 1 [tex](2x - 3)> 0[/tex]

[tex]9 + 2x - 3 = 7\\2x = 7 + 3-9\\2x = 1\\x = 0.5[/tex]

Case 2 [tex](2x - 3) <0[/tex]

[tex]9 - (2x - 3) = 7\\-2x + 3 = 7-9\\-2x = 7-9-3\\-2x = -5\\x = 2.5[/tex]

For the equation

2) [tex]3 + | 2x - 4 | = 15[/tex]

we have 2 cases

Case 1 [tex](2x - 4)> 0[/tex]

[tex]3 + 2x - 4 = 15\\2x = 15 + 4-3\\2x = 16\\x = 8[/tex]

Case 2 [tex](2x - 4) <0[/tex]

[tex]3 - (2x - 4) = 15\\-2x +4 = 15-3\\-2x = 15-3-4\\-2x = 8\\x = -4\\[/tex]

Answer:

Step-by-step explanation:

0.24 is greater than 0.17, and therefore J's getting a strike next game is more likely.

The event that is more likely is Juanita gets a strike next game.

Probability is the likelihood that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that Juanita would have a strike is higher than that of Nina. Thus, it is more likely that  Juanita gets a strike next game.

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Answer:

The measure of arc HD is 20°

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

In the triangle of the figure , the measure of the third  interior angle is equal to

180°-92°-38°= 50°

50°=(1/2)[(102+18)°-arc HD]

100°=[120°-arc HD]

arc HD=120°-100°=20°

Answer:

 arc HD = 20°

Step-by-step explanation:

Let point N be the point where secant RL intersect the circle, point M be the point of intersection for chords NL and KH, and point S be the vertex of the triangle formed by secants KH and RD.

It is given that m∠SRM = 38∘ and m∠RMS = 92∘. Use the Triangle Sum Theorem to determine m∠MSR.

m∠MSR = 180° − 92∘ − 38∘  = 50∘

It is also given that mPN = 18∘ and mNK = 102∘. So, mPK = 18∘ + 102∘ = 120∘.

If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs. So,  

m∠MSR= 1 /2 (mPK − mHD)

Substitute the known values and solve for mHD.

50∘ = 1/2 (120∘ − mHD)

Multiply by 2.

100 = 120∘ − mHD

Simplify.

mHD = 20

Therefore, the measure of arc HD is 20∘.

Answer:

  640 = 0.80·j

Step-by-step explanation:

Let j represent the cost of Jocelyn's computer (in dollars). Adriana's computer cost 20% less, so has a cost that is 0.80·j. We are told that amount is $640, so we can write the equation ...

  640 = 0.80·j

Given an implication of the form [tex]P\implies Q[/tex]

The equivalent implication is [tex]\lnot Q \implies \lnot P[/tex]

So, you have to negate both propositions and invert the order:

If a triangle is not isosceles, then it's not equilateral.

Answer:  [tex]\bold{B)\quad \dfrac{x-2}{x+1}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x^2+5x-14}{x^2+8x+7}\\\\\\=\dfrac{(x+7)(x-2)}{(x+7)(x+1)}\\\\\\=\dfrac{x-2}{x+1}[/tex]

Answer:

Part 1) The volume of the composite figure is [tex]620.7\pi\cm^{3}[/tex]

Part 2) The surface area of the composite figure is [tex]273\pi\ cm^{2}[/tex]

[tex]V=620.7\pi\cm^{3}, S=273\pi\ cm^{2}[/tex]

Step-by-step explanation:

Part 1) Find the volume of the composite figure

we know that

The volume of the figure is equal to the volume of a cone plus the volume of a hemisphere

Find the volume of the cone

The volume of the cone is equal to

[tex]V=\frac{1}{3} \pi r^{2} h[/tex]

we have

[tex]r=7\ cm[/tex]

Applying Pythagoras Theorem find the value of h

[tex]h^{2}=25^{2} -7^{2} \\ \\h^{2}= 576\\ \\h=24\ cm[/tex]

substitute

[tex]V=\frac{1}{3} \pi (7)^{2} (24)[/tex]

[tex]V=392 \pi\cm^{3}[/tex]

Find the volume of the hemisphere

The volume of the hemisphere is equal to

[tex]V=\frac{4}{6}\pi r^{3}[/tex]

we have

[tex]r=7\ cm[/tex]

substitute

[tex]V=\frac{4}{6}\pi (7)^{3}[/tex]

[tex]V=228.7\pi\cm^{3}[/tex]

therefore

The volume of the composite figure is equal to

[tex]392 \pi\cm^{3}+228.7\pi\cm^{3}=620.7\pi\cm^{3}[/tex]

Part 2) Find the surface area of the composite figure

we know that

The surface area of the composite figure is equal to the lateral area of the cone plus the surface area of the hemisphere

Find the lateral area of the cone

The lateral area of the cone is equal to

[tex]LA=\pi rl[/tex]

we have

[tex]r=7\ cm[/tex]

[tex]l=25\ cm[/tex]

substitute

[tex]LA=\pi(7)(25)[/tex]

[tex]LA=175\pi\ cm^{2}[/tex]

Find the surface area of the hemisphere

The surface area of the hemisphere is equal to

[tex]SA=2\pi r^{2}[/tex]

we have

[tex]r=7\ cm[/tex]

substitute

[tex]SA=2\pi (7)^{2}[/tex]

[tex]SA=98\pi\ cm^{2}[/tex]

Find the surface area of the composite figure

[tex]175\pi\ cm^{2}+98\pi\ cm^{2}=273\pi\ cm^{2}[/tex]

Answer:

34,623

Step-by-step explanation:

427,113 + 38,264 = 465377

500,000 - 465377 = 34,623 books in December must go out to meet the librarian's goal.

The solution is the point where the two lines meet. The answer is D.

3. replace x with 4 and solve:

3(4) - 5 = 12 -5 = 7

The answer is 7

4. Replace x with 6 in the equation for g(x) first:

2(6) -5 = 12-5 = 7

Now replace x with 7 in the equation for f(x)

2(7) +1 = 14 +1 = 15

The answer is 15

Answer:

  m∠QRS = 30°

Step-by-step explanation:

An inscribed angle has half the measure of the intercepted arc.

  (arc QS)/2 = 60°/2 = 30°

The measure of angle QRS is 30°.

ANSWER

(1,4)

(-∞,-3)

EXPLANATION

The interval where a portion of the graph is below the x-axis is where the graph is negative.

From the graph , the curve is below the x-axis on the interval (-∞,-3). Hence the graph is negative on this interval.

Also the graph is below the x-axis on the interval (1,4). This is also another interval where the graph is negative.

Answer:

  BF = 30

Step-by-step explanation:

Each midsegment is half the length of the parallel side of the triangle. CE is 60 and is parallel to BF, so BF = 60/2 = 30.

Answer:

[tex]\large\boxed{4\vec{u}+3\vec{v}=<-26,\ 26>}[/tex]

Step-by-step explanation:

[tex]\vec{u}=<-5,\ 2>;\ \vec{v}=<-2,\ 6>\\\\4\vec{u}=<(4)(-5),\ (4)(2)>=<-20,\ 8>\\\\3\vec{v}=<(3)(-2),\ (3)(6)>=<-6,\ 18>\\\\4\vec{u}+3\vec{v}=<-20,\ 8>+<-6,\ 18>=<-20+(-6),\ 8+18>=<-26,\ 26>[/tex]

The result of the vector addition and scalar multiplication operation 4u + 3v, with u=<-5,2> and v=<-2,6>, is <-26,26>.

Given the vectors u=<-5,2> and v=<-2,6>, we can compute the expression 4u + 3v by performing vector addition and scalar multiplication.

First, we multiply the vectors by their respective scalars, which results in 4u = 4*(-5,2) = <-20,8> and 3v = 3*(-2,6) = <-6,18>.

Then we add the resulting vectors together. The x-components add together to produce the new x-component and the y-components add together to produce the new y-component. So 4u + 3v = <-20,8> + <-6,18> = <-26,26>.

This demonstrates the distributive property and the principles of vector addition and scalar multiplication.

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Answer:

is this all apart of the answers or separate questions??

Step-by-step explanation:

1. B

2.C

3.C

4.A

5.D

Answer:

Step-by-step explanation:

You might see this a bit easier if you change the 5/4 * pi into degrees.

pi/180 = 5/4*pi / x                   This is the proportion. Change 5/4 into a decimal

pi/180 = 1.25 *pi / x                 Cross multiply

x * pi = 1.25 pi * 180                Divide by pi

x = 1.25 * 180

x = 225 degrees.

The fraction of the area of the sector is angle/360

The fraction of the area  of the sector is 225/360  

The fraction of the area area of the sector is 5/8    Reduced.

225: 3*3*5*5

360 = 2*2*2*5*3 *3  

Cancel out the common factors

3 * 3 * 5

which leaves 5/8

Two

-3x^2 + 5x - 2 - 2x^2 + 4x + 2

- 5x^2 + 9x (the 2's cancel)

a = - 5

b = 9

c = 0

ANSWER

The radius is 25 inches

EXPLANATION

From the diagram, the radius of the circle is AC.

From the Pythagoras Theorem,

[tex] {r}^{2} = {7}^{2} + {24}^{2} [/tex]

[tex]r^{2} = 49 + 576[/tex]

Simplify

[tex]r^{2} = 625[/tex]

Take positive square root,

[tex]r = \sqrt{625} [/tex]

[tex]r = 25[/tex]

Hence the radius is 25 inches

Answer:

The ratio is equal to [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

Let

x----> the amount spent on advertising

y----> the amount spent on its website

The ratio is equal to x/y

Remember that

[tex]0.75=\frac{3}{4}[/tex]

so

[tex]\frac{1}{(3/4)}=\frac{4}{3}[/tex]

Answer:

26 + 10i is your answer.

Answer:

surface area of a sphere= 4pi*r^2

S.A when radius is 7 is:

=4pi*(7)^2

=196pi cm^2

if you multiply radius by 4, the equation becomes:

4pi*(4r)^2

=4pi*16r^2

=64pi*r^2

substitute 7 into equation:

=64pi*(7)^2

=64pi*49

=3136pi cm^2

Divide new S.A. by old S.A. to show effect:

=3136pi/196pi

=16

If the radius is multiplied by 4, the effect on the surface area is that it is 16 times the surface area of the sphere where the radius is not multiplied.

If the radius of a sphere of radius 7 cm is multiplied by 4, then its surface area is increased 16 times than the initial surface area.

Suppose that radius of the considered sphere is of 'r' units.

Then, its surface area S would be:

[tex]S = 4\pi r^2 \: \rm unit^2[/tex]

For this case, we're specified that:

We've to find the effect on the surface area of the sphere.

Initial surface area:

[tex]S_i = 4\pi r^2 = 4 \pi (7)^2 \: \rm unit^2[/tex]
Final surface area:

[tex]S_f = 4\pi r^2 = 4 \pi (4 \times 7)^2 = 4^2 \times [4 \pi (7)^2] \: \rm unit^2\\\\S_f =16 \times S_i[/tex]

Thus, if the radius of a sphere of radius 7 cm is multiplied by 4, then its surface area is increased 16 times than the initial surface area.

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